This lesson has an introductory activity that uses bottles of various shapes to help students understand rate of change. The lesson then develops the concept of the average rate of change between two points on a curve.

This lesson has an introductory activity that uses bottles of various shapes to help students understand rate of change. The lesson then develops the concept of the average rate of change between two points on a curve. Finally, it examines instantaneous rate of change: The rate of change function is used to estimate the rate of change at a particular point. This function is used along with the calculator to make computing the rate of change fast and easy for students. The development of this function helps students understand what is meant by instantaneous rate of change and lays a firm foundation for the study of the derivative in calculus. In addition to the lesson plan, the site includes ideas for assessment, teacher discussion, extensions of the lesson, additional resources, and a discussion of the mathematical content. The lesson plan is accompanied by video clips illustrating lesson procedures. The user should first locate the Bottles and Divers lesson and then access the appropriate video clips at the PBS TeacherSource website. The video player necessary to view the video clips can be downloaded for free from the site. (Author/pk)